A molten salt reactor (MSR) is characterized by simultaneously using liquid fuel salt as both the nuclear fuel and coolant. The redistribution of delayed neutron precursors (DNPs) makes the transient behavior of MSRs different from traditional solid-fuel reactors. In this study, a 3D coupled neutronics/thermal hydraulics code, MOREL2.0, was employed to analyze a liquid-fuel Thorium Molten Salt Reactor (TMSR-LF) under perturbations of fuel pump start-up and coast-down and by overheating and overcooling the inlet fuel temperature. Some transient processes were simulated to provide guidance for the future design and optimization of TMSR-LFs. In response to the perturbations, reactivity was lost and gained in the pump start-up and coast-down, respectively. Overheating the inlet fuel temperature introduced negative reactivity, and TMSR-LF maintained a safety state, while overcooling the inlet fuel temperature resulted in positive reactivity. Overcooling by 70 K produced a supercritical transient condition and a rapid increase in power within a short period, which was followed by a decrease in power due to negative temperature feedback. The transient results demonstrate that the negative temperature feedback coefficients guarantee TMSR-LF inherent safety and the variation range of temperature stay within the safety margin.